A computationally efficient correlated mixed probit model for credit risk inference

Mixed probit models are widely applied in many fields where prediction of a binary response is of interest. Typically, the random effects are assumed to be independent but this is seldom so for many real applications. In the credit risk application that is considered in the paper, random effects are present at the level of industrial sectors and they are expected to be correlated because of interfirm credit links inducing dependences in the firms’ risk to default. Unfortunately, existing inferential procedures for correlated mixed probit models are computationally very intensive already for a moderate number of effects. Borrowing from the literature on large network inference, we propose an efficient expectation–maximization algorithm for unconstrained and penalized likelihood estimation and derive the asymptotic standard errors of the estimates. An extensive simulation study shows that the approach proposed enjoys substantial computational gains relative to standard Monte Carlo approaches, while still providing accurate parameter estimates. Using data on nearly 64000 accounts for small and medium-sized enterprises in the UK in 2013 across 13 industrial sectors, we find that accounting for network effects via a correlated mixed probit model increases significantly the default prediction power of the model compared with conventional default prediction models, making efficient inferential procedures for these models particularly useful in this field.